Problem: Rewrite as a simplified fraction. ${3.5\overline{13} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3513.1313...\\ 10x &= 35.1313...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3478}$ ${x = \dfrac{3478}{990}} $ ${x = \dfrac{1739}{495}} \text{or} {3 \dfrac{254}{495}}$